Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling
, Óscar E. Coronado-Hernández 2,*, Vicente S. Fuertes-Miquel 3, Mohsen Besharat 4 and Helena M. Ramos 5
Josep Maria Bofill
Round 1
Reviewer 1 Report
The manuscript discusses an interesting phenomenon related to transient flows in closed conduits that have been evaluated since the 1976's paper by Martin. However, the manuscript is not ready to be acceptable as issues need the authors' attention.
L55 onward: Is the ODE approach used by the authors indeed one-dimensional? Since there is no spatial dimension, and the other referred methods (2D, 3D) refer to multiple physical dimensions, I think the statement is ambiguous and needs your attention.
L66, Major issue: The statement explains what the manuscript aims to achieve, but does not justify why this is needed. Given the existing methods to solve these equations, why do you need to propose an NR method? Is it because of efficiency? If so, this gain in efficiency needs to be demonstrated systematically. Otherwise, the justification for the work is simply not stated in the introduction.
Methodology, Major issue: This ODE formulation with no air release is relatively trivial for an NR solution. I would like to see a more complete version of the method in which air is released from the system (i.e., orifice flow) during the compression.
Results, Major issue: The approach is tested against geometries similar to Martin (1976). Two experimental variables (xo and Po) were tested for a total of 6 cases, but the experimental setup is also pretty similar to that study. I would like to see more experimental cases considered, for instance, making varying sections downstream from the pressure transducer dry so that the amount of air in the system could increase into much larger values for assessing the method.
Author Response
Please see attached file
Author Response File: 
Author Response.pdf
Reviewer 2 Report
See the attached PDF file.
Comments for author File: Comments.pdf
Author Response
Please see attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
1) While the authors recommend using the isothermal solution as a first guess for the cases when k<>1, please explain in the manuscript whether or not it is possible that the NR method diverges.
2) Fig.2 - L_f = L_o is somewhat unclear as it implies that the initial length and final lengths are the same for isothermal compression.
3) L187, you are referring to eq. 10 or 11?
4) L209 should be "3. Analysis of Results and Discussion". Also, you do
5) L263 - "tis" should be "its"
6) Sensitivity analysis section: please draw parallels between the discussion presented in section 3.2 and the results by Martin 1976, who arrived at the same observations as the present manuscript. It is impressive to me that one of the first papers to deal with the problem presented by the authors is not cited in this work.
Author Response
Dear Reviewer:
Thank you for your comments. Please see attached file.
Author Response File: Author Response.pdf
